evaluate the expression

Question

evaluate the expression 

(-2-3i)/(1-2i)

the real number a equals?

the real number b equals?

Answer 1

Hi Dalia,

 

(-2-3i)/(1-2i)

 

multiply the numerator and denominator by (1+2i)

 

(-2-3i)(1+2i)/(1-2i)(1+2i)

 

(-2-4i-3i-6i²)/(1)²-(2i)²

 

(-2-7i+6)/(1-4i²)      (i²=-1)

 

(4-7i)/(1+4)

 

(4-7i)/5

 

4/5-7i/5

 

a+bi=4/5-7i/5

 

a=4/5  and b=-7/5

Answer 2

With division of complex numbers, you cannot leave an i in the bottom. To get rid of it you multiply both the numerator and denominator by the conjugate of the denominator. 

A conjugate is where you change the sign of the b term. So in a + bi, the conjugate would be a - bi.

 

So you are multiplying {(-2-3i)(1+2i)} / {(1-2i)(1+2i)}

 

Using foil, on the top you get {-2 - 4i - 3i -6i²} / {1 + 2i - 2i -4i²}

 

Then combining like terms, and replacing i² as -1, we get {-2 -7i +6} / {1 +4}

which then further combines to (4 - 7i)/5

 

Splitting them apart we get 4/5 - (7/5)i

So a = 4/5 and b = -7/5